This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fnmap

Description: Set exponentiation has a universal domain. (Contributed by NM, 8-Dec-2003) (Revised by Mario Carneiro, 8-Sep-2013)

		Ref	Expression
	Assertion	fnmap	$⊢ ↑_{𝑚} Fn (V \times V)$

Step	Hyp	Ref	Expression
1		df-map	$⊢ ↑_{𝑚} = (x \in V, y \in V ⟼ \{f \| f : y ⟶ x\})$
2		mapex	$⊢ (y \in V \land x \in V) \to \{f \| f : y ⟶ x\} \in V$
3	2	el2v	$⊢ \{f \| f : y ⟶ x\} \in V$
4	1 3	fnmpoi	$⊢ ↑_{𝑚} Fn (V \times V)$